Simplify the following expression: $z = \dfrac{-8a^2 - 72a}{48a^2 + 80a}$ You can assume $a \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-8a^2 - 72a = - (2\cdot2\cdot2 \cdot a \cdot a) - (2\cdot2\cdot2\cdot3\cdot3 \cdot a)$ The denominator can be factored: $48a^2 + 80a = (2\cdot2\cdot2\cdot2\cdot3 \cdot a \cdot a) + (2\cdot2\cdot2\cdot2\cdot5 \cdot a)$ The greatest common factor of all the terms is $8a$ Factoring out $8a$ gives us: $z = \dfrac{(8a)(-a - 9)}{(8a)(6a + 10)}$ Dividing both the numerator and denominator by $8a$ gives: $z = \dfrac{-a - 9}{6a + 10}$